Commun. Theor. Phys. 59 (2013) 528–532 Vol. 59, No. 5, May 15, 2013 Asymptotic Study to the N-Dimensional Radial Schr¨odinger Equation for the Quark-Antiquark System Ramesh Kumar ∗ and Fakir Chand † Department of Physics, Kurukshetra University, Kurukshetra-136119, India (Received November 14, 2012; revised manuscript received February 4, 2013) Abstract Here an asymptotic study to the N-dimensional radial Schr ¨ odinger equation for the quark-antiquark inter- action potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out. The complete energy spectra of the consigned system is obtained by computing and adding energy eigenvalues for ground state, for large “ r” and for small “ r”. From this analysis, the mass spectra of heavy quarkonia is derived in three dimensions. Our analytical and numerical results are in good correspondence with other experimental and theoretical studies. PACS numbers: 03.65.Ge Key words: N-dimensional radial Schr¨ odinger equation, quarkonium potential, eigenvalue, eigenfunction 1 Introduction Since from the development of the radial Schr¨ odinger equation (SE) in quantum mechanics, its solutions play a major role in many fields of modern physics. For studying the behavior of several physical problems in physics, we require to solve the SE. The solutions to the SE can be established only if we know the confining potential for a particular physical system. The confining potentials may have various forms depending upon the interaction of the particles within the system. Till now, there are only a few confining potentials, like the harmonic oscil- lator and the hydrogen atom, for which solutions to the SE are found exactly. In past, numerous analytic and nu- merical formulations such as the shifted 1/N expansion method, [1] super-symmetric quantum mechanics, [2] the WKB method, [3] Hill determinant method, [4] Nikiforov– Uvarov method, [5] asymptotic iteration method (AIM) [6] and numerical methods [7−10] have been developed for ob- taining the exact or approximate solutions of confining potentials. [11−15] For some times now, the AIM is increasingly becom- ing popular among researchers for finding the solutions to the SE for a variety of potentials. It has successfully been applied to the second order homogeneous differential equations, which have wide applications to many problems in physics, such as the equations of Hermite, Laguerre, Legendre and Bessel. [6] The AIM had also been employed to solve exactly the SE for the Morse potential, [16] the P¨ osch–Teller potential, the harmonic oscillator potential, the complex cubic potential [6] and the anharmonic oscil- lator potentials. [17] Further, with the help of AIM, one can investigate the asymptotic solutions of the SE for the quark-antiquark system where the underlying interaction potential is of Cornell type i.e. Coulomb potential with linear terms. In this potential, the Coulomb and the linear terms are liable for the interaction at small distances and confinement re- spectively. The study of this potential is of particular interest for detecting the mass spectra for coupled states and for characterizing the electromagnetic characteristics of mesons. In past, this type of potential has been inves- tigated by many authors using different techniques. [18−22] Here in the present work, we modify the Cornell poten- tial by adding the harmonic term. The resultant quark- antiquark interaction potential, also known as quarkonium potential, is written as U (r)= ar 2 + br − c r , a> 0 . (1) A literature survey reveals that most of the research work for studying the SE is confined for two and three- dimensional systems. However, recently, some authors have enhanced the scope of such studies to N-dimensional space. [23−27] These higher dimensional studies of the SE can provide detailed information about the behavior of problems. Moreover, one can also conveniently derive the eigenvalue spectra in lower dimensions from the general- ized higher dimensional results. Keeping in view the importance of generalized results, we extend the dimensionality limit i.e. we obtain the so- lutions to the SE in N-dimensional space for potential (1) by using the AIM. This effective and simple method can produce good results for both the exactly and not-exactly solvable physical problems. The adjustment of the paper is as follows: Sec. 2 gives a brief description of the AIM. The asymptotic solution of * Corresponding author, E-mail: rameshkumar.bibiyan@gmail.com † E-mail: fchand@kuk.ac.in c  2013 Chinese Physical Society and IOP Publishing Ltd http://www.iop.org/EJ/journal/ctp http://ctp.itp.ac.cn